In this paper, to address the WSR maximization problem for the multi-hop
RIS-aided multi-user systems, a problem-tailored low-complexity and
globally convergent algorithm based on block minorization-maximization
(BMM) [1]}, [2]} is proposed.
The proposed BMM-based algorithm works for both the continuous-phase
and the discrete-phase schemes for RISs and can be easily generalized
to other RIS-related system design problems. Theoretically, we show
that the sequence of iterates generated by the proposed algorithm
converges to a KKT point of the WSR maximization problem. The superiority
of the proposed BMM approach over existing algorithms under a single-hop
setting and the performance improvement gained with multi-hop RISs
are both demonstrated through numerical simulations, while the influence
of the quantization level on the discrete phases is also showcased.
